The problem with a third party is that the whole job description for incumbents of either party is to get reelected. Let me illustrate this in a different way. In the soft drink industry, Coke and Pepsi dominate sales. Their high sales allow for massive advertising campaigns. Other than small regional powers, no one can compete with Coke and Pepsi. They have a rivalry with each other, but they completely destroy any smaller competition.
It is the same for Democrats and Republicans. They want to defeat the other party, but most vital is to eliminate all other competition. That way, there are only two real contenders for each seat. Each election, less than 100 House seats are competitive. That allows massive advertising in a few places. No third party could dream of competing with that.
A third party president would be the quickest way to unify Congress. They would destroy any chances that president would have of accomplishing anything.
I can only think of a few ways to lower the polarization of the House of Representatives. They need to eliminate the gerrymandered districts because they just protect the incumbent. Protecting the incumbent keeps the house full of the fringes of both parties. Anyone trying to run from the middle would be wiped out by the more "ideologically pure" candidates.
Coupled with redistricting could be to lower the number of representatives in the House. That would give larger districts and make them harder to gerrymander.
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